FINITE ELEMENT ANALYSIS AND RELIABILITY STUDY OF MULTI ...

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University of Kentucky Master's Theses Graduate School

2004

FINITE ELEMENT ANALYSIS AND RELIABILITY STUDY OF MULTI-FINITE ELEMENT ANALYSIS AND RELIABILITY STUDY OF MULTI-

PIECE RIMS PIECE RIMS

Sandeep Chodavarapu University of Kentucky, [email protected]

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ABSTRACT OF THESIS

FINITE ELEMENT ANALYSIS AND RELIABILITY STUDY OF MULTI-PIECE RIMS

Multi-piece wheels or rims used on large vehicles such as trucks, tractors, trailers, buses and off-road machines have often been known for their dangerous properties because of the large number of catastrophic accidents involving them. The main causes for these accidents range from dislocation of the rim components in the assembly, mismatch of the components, manufacturing tolerances, corrosion of components to tires. A finite element analysis of a two-piece rim design similar to one manufactured by some of the prominent rim manufacturers in the USA is undertaken. A linear static deformation analysis is performed with the appropriate loading and boundary conditions. The dislocation of the side ring with respect to the rim base and its original designer intent position is established using simulation results from ANSYS and actual rim failure cases. Reliability of the multi-piece rims is analyzed using the failure data provided by the rim manufacturers in connection with a lawsuit (Civil Action No. 88-C-1374). The data was analyzed using MINITAB. The effect of an OSHA standard (1910.177) on servicing multi-piece rims was studied for change in failure patterns of different rims. The hazard functions were plotted and failure rates were calculated for each type of rim. The failure rates were found to be increasing suggesting that the standard had minimal effect on the accidents and failures. The lack of proper service personnel training and design defects were suggested as the probable reasons for the increasing failure rates. Keywords: Multi-piece rims, accidents, finite element analysis, reliability, OSHA.

Sandeep Chodavarapu

Date:12/09/2004

Copyright © Sandeep Chodavarapu 2004


By

Sandeep Chodavarapu

Dr.O.J.Hahn -------------------------------------------

(Director of Thesis)

Dr. George Huang -------------------------------------------

(Director of Graduate Studies)

12/09/2004 -------------------------------------------

(Date)

RULES FOR THE USE OF THESES

Unpublished theses submitted for the Master’s degree and deposited in the University of Kentucky Library are as a rule open for inspection, but are to be used only with due regard to the rights of the authors. Bibliographical references may be noted, but quotations or summaries of parts may be published only with the permission of the author, or with the usual scholarly acknowledgements. Extensive copying or publication of the thesis in whole or in part also requires the consent of the Dean of the Graduate School of the University of Kentucky.

THESIS

Sandeep Chodavarapu

The Graduate School

University of Kentucky

2004


THESIS

A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Mechanical Engineering in the

College of Engineering at the University of Kentucky

By

Sandeep Chodavarapu

Lexington, Kentucky

Director: Dr.O.J.Hahn, Professor of Mechanical Engineering

Lexington, Kentucky

2004

Copyright © Sandeep Chodavarapu 2004

In loving memory of my mother, Lakshmi Chodavarapu

ACKNOWLEDGEMENTS

Guru Brahma Gurur Vishnu Guru Devo Maheshwaraha

Guru Saakshat Para Brahma Tasmai Sree Gurave Namaha

Meaning: Guru (the teacher) is verily the representative of Brahma (the creator), Vishnu (the sustainer) and Shiva (the destroyer). He creates, sustains knowledge and destroys the weeds of ignorance. I salute such a Guru.

The above Sanskrit verse is well known in Indian culture to truly honor a Guru (teacher). I

am deeply indebted to my Guru, Dr.O.J.Hahn for providing me an opportunity to grow in

every aspect of my life under his able guidance. I thank him from the bottom of my heart

for having given me a chance to be a part of this research. I have greatly benefited from

my long hours of interaction with him each day. He has been a father figure to me ever

since I set foot in the United States of America. He has pulled me out of many ignorant

situations and has immensely supported and inspired me during my personal tragedy. I am

at loss of words to truly honor such a great and exceptional man.

I am deeply obliged to Dr. Kozo Saito and Dr. J.D. Jacob for having agreed to be on my

Thesis Committee. They have provided outstanding insights that have guided me to deliver

a much better work. Their critical review is gratefully acknowledged.

It is only the unparalleled love, support and vision of my parents that has made this work a

reality. I dedicate this work to my mother, Lakshmi Chodavarapu who has been my source

of strength since childhood. She laid a strong foundation to my future, inspired me to take

up engineering as a career and has sacrificed her life for my studies. I wish she was alive to

see my work. I hope to keep up to her aspirations and pray for her soul to rest in almighty

peace. My father, Saradhi Chodavarapu is another great person without whom this

iii

document would not have been a reality. He has endured many a difficult and testing times

in life to help me achieve my goals. My brother, Kuldeep Chodavarapu deserves all the

love and credit for his constant support and encouragement. Finally, I would like to thank

all my friends who have understood and motivated me during the course of this work. It is

their unconditional love that has sustained me through the last couple of years.

iv

TABLE OF CONTENTS

ACKNOWLEDGMENTS…………………………………………………………...…….iii

LIST OF TABLES…………………………………………………………………...……vii

LIST OF FIGURES……………………………………………………………………....viii

LIST OF FILES…………………………………………………………………………….x

CHAPTER 1: INTRODUCTION………………………………………………………..…1

1.1 BACKGROUND………………………………………………………………….....1

1.2 WHEEL AND RIM ASSEMBLIES………………………………………………...2

1.3 OBJECTIVE………………………………………………………………………...5

CHAPTER 2: REVIEW OF PUBLISHED LITERATURE……………………………….7

2.1 BACKGROUND…………………………………………………………………....7

2.2 STRESS ANALYSIS……………………………………………………………….7

CHAPTER 3: FINITE ELEMENT ANALYSIS………………………………………….10

3.1 INTRODUCTION TO FEA………………………………………………………..10

3.2 INTRODUCTION TO ANSYS…………………………………………………….11

3.3 INTRODUCTION TO PRO/E……………………………………………………..13

3.4 MODELING USING PRO/E………………………………………………………13

3.5 ANALYSIS OF TWO-PIECE RIM………………………………………………..16

3.6 RESULTS AND DISCUSSION……………………………………………………18

CHAPTER 4: RELIABILITY ANALYSIS……………………………………………….25

4.1 STATISTICAL DISTRIBUTIONS………………………………………………...25

4.1.1 Exponential Distribution……………………………………………………….25

v

4.1.2 Log Normal Distribution………………………………………………………25

4.1.3 Weibull Distribution…………………………………………………………...26

4.2 GOODNESS-OF-FIT TESTS……………………………………………………...27

4.3 FAILURE DATA OF DIFFERENT TYPES OF RIMS……………………………29

4.4 ANALYSIS OF DATA USING MINITAB………………………………………..36

4.5 RESULTS AND DISCUSSION…………………………………………………....42

CHAPTER 5: CONCLUSIONS…………………………………………………………..47

5.1 SUMMARY………………………………………………………………………...47

5.2 CONCLUSIONS…………………………………………………………………...47

APPENDIX A: POST PROCESSING FROM MINITAB………………………………..51

APPENDIX B……………………………………………………………………………..64

REFERENCES…………………………………………………………………………….66

VITA………………………………………………………………………………………67

vi

LIST OF TABLES

Table 4.1: Accident statistics for different types of rims before OSHA Guideline……….30

Table 4.2: Accident statistics for different types of rims after OSHA Guideline…………31

Table 4.3: Accident statistics for single-piece rims before OSHA Guideline…………….31

Table 4.4: Accident statistics for single-piece rims after OSHA Guideline………………32

Table 4.5: Accident statistics for single-piece rims (non-rubber failures)………………...32

Table 4.6: Results from analysis of ‘RH 50’ type rim data using MINITAB……………..42

Table 4.7: Results from analysis of two-piece type rim data using MINITAB…………...42

Table 4.8: Results from analysis of three-piece type rim data using MINITAB………….43

Table 4.9: Results from analysis of unknown type rim data using MINITAB……………43

Table 4.10: Failure Rates of different types of rims before and

after the OSHA Standard……………………………………………………..45

Table 4.11: Beta values comparison of multi-piece rims with different engineering

components………………………………………………………………….46

vii

LIST OF FIGURES

Figure 1.1: Rim……………………………………………………………………………..3

Figure 1.2: Two-piece rim outline………………………………………………………….4

Figure 3.1: SOLID95 3-D 20-Node Structural Solid……………………………………...12

Figure 3.2: Tube-Type Demountable Rim Assembly (two-piece)………………………..14

Figure 3.3: Rim Base……………………………………………………………………...15

Figure 3.4: Split Side Ring………………………………………………………………...15

Figure 3.5: Two degree model of rim imported into ANSYS…………………………….17

Figure 3.6: Elements generated using the meshing option in ANSYS……………………17

Figure 3.7: ANSYS plot of the deformed shape of the rim assembly…………………….18

Figure 3.8: ANSYS plot of the deformed and un-deformed shape of the rim assembly….19

Figure 3.9: ANSYS plot of the Von-Mises stress profile of the rim assembly. ………….19

Figure 3.10: Original fit of the components in a multi-piece rim…………………………21

Figure 3.11: Dislocation of the ring portion from the rim base at position 1……………..22

Figure 3.12: Rotational dislocation of ring portion from rim base at position 2………….23

Figure 3.13: Separation of the side ring from the rim base from ANSYS simulation…….24

Figure 3.14: Dislocation of side ring from rim base from ANSYS simulation………...…24

Figure 4.1: Graph for all the different types of rim accidents…………………………….33

Figure 4.2: Accident Curves for RH 5 rims………………………………………………33

Figure 4.3: Accident Curves for Two Piece rims………………………………………….34

Figure 4.4: Accident Curves for Three Piece rims………………………………………...34

Figure 4.5: Accident Curves for Single Piece rims………………………………………..35

Figure 4.6: Accident Curves for Unknown type rims……………………………………..35

Figure 4.7: D.O1 plot for RH 5 rim accident data (Pre OSHA Standard)…………………38

Figure 4.8: D.O plot for RH 5 rim accident data (Post OSHA Standard). ………………..38

viii

Figure 4.9: D.O plot for two-piece rim accident data (Pre OSHA Standard)……………..39

Figure 4.10: D.O plot for two-piece rim accident data (Post OSHA Standard). …………39

Figure 4.11: D.O plot for three-piece rim accident data (Pre OSHA Standard). ………...40

Figure 4.12: D.O plot for three-piece rim accident data (Post OSHA Standard)…………40

Figure 4.13: D.O plot for unknown rim accident data (Pre OSHA Standard)…………….41

Figure 4.14: D.O plot for unknown rim accident data (Post OSHA Standard)…………...41

Figure 5.1: Regenerated side ring and rim base assembly………………………………...48

Figure 5.2: Dislocation of side ring on regenerated assembly…………………………….48

Figure B.1: Tire rim assembly…………………………………………………………….65

Figure B.2: Dislocation along a portion of the rim circumference………………………..66

1 - Distribution Overview.

ix

LIST OF FILES

Chodavarapu.pdf ………………………………………………………….…………...2 MB

x

CHAPTER ONE

INTRODUCTION

1.1 BACKGROUND

The earliest known wheel to the modern civilization was believed to be over fifty-five

hundred years old, found in archeological excavations in what was Mesopotamia. Over the

centuries, wheels have undergone gargantuan changes in manufacturing and application

technology. We have moved over from the initial wooden wheels to manufacturing steel

wheels to using different alloys for the same purpose for various functions and advantages.

Successful designs have been established after years of experience, research and testing.

These improvements have been aided by the development of several new scientific and

analytical methods. The exact operating conditions can be simulated by finite element

methods and computer programs. The reliability and safety considerations in operating a

wheel can be configured with diverse analyses methods. The wheel over the centuries has

come to become an inseparable part of human civilization. Wheels are also one of the most

important components of automobiles from the view point of structural safety. As a result,

wheels must be certified to have sufficient safety margins even under severe driving and

operating conditions. Moreover, since other requirements such as lighter weight or more

attractive design make the configuration of the wheel more complicated and sophisticated,

it has become necessary to perform rigorous strength evaluations of the wheel in detail

when a new wheel design is developed. A well designed wheel is the foundation which

adds strength, stability and durability to a tire. Hence, the increased urge to make them

safer and reliable.

1

1.2 WHEEL AND RIM ASSEMBLIES

The wheel, according to the SAE standard, SAE J393 OCT 91 is defined as a rotating

load-carrying member between the tire and the hub. The main components of a wheel are

the rim, the tire and the disk or the spokes. The rim and the tire in a wheel assembly are

specially matched components. The hub is the rotating member that represents the

attachment face for wheel discs. The rim is defined as the supporting member for the tire

or tire and the tube assembly. The disc wheel is a permanent combination of the rim and

the disc. The disc or the spider is defined as the center member of a disc wheel. There have

been many rim designs in use. They can be broadly classified into- a single piece rim and a

multi-piece rim. A single-piece rim is a continuous one-piece assembly. The multi-piece

rims are essentially two or more pieces assembled together according to a concentric fit

design. The assembly consists of a rim base and either a side ring or a side and lock ring

depending on the number of pieces making the whole rim. In two-piece assemblies, the

side ring retains the tire on one side of the rim. The fixed flange supports the other

side. The side ring in a two-piece assembly could be either continuous or split. The split

side ring is designed so that it acts as a self-contained lock ring as well as a flange. Some

of the rims have a drop centre, where the central portion of the rim base is a drop of a

certain angle from the main contour of the rim. The area where the drop starts is usually a

hump which is of two types- Flat Hump (FH) or the Round Hump (RH). The rim is

designated by either one of these along with the angle of the drop. A couple of these types

have been illustrated in the figure below.

2

Dimensions: A – Rim width P – Bead seat width

B – Flange width R1 – Flange compound radius

D – Rim diameter R2 – Flange radius

D2 – Rim inside diameter R4 – Well top radius

G – Flange height FH – Flat hump

H – Well depth RH – Round hump

M – Well position β – Bead seat angle

Figure 1.1: Rim

3

Fixed Flange

Side Ring Bead Seat Area

Rim Base

Figure 1.2: Two-piece rim outline.

In three-piece assemblies, the flange or continuous side ring supports the tire on one side

of the rim. The continuous side ring is, in turn, held in place by a separate split lock ring.

All lock rings are split. In three-piece assemblies, the lock ring is designed to hold the

continuous side ring on the rim.

The safety or efficient operation of the rims relies to a large extent on the component parts

of the rims. Some of the main causes for concern are the deformation of the rim base and

the side ring. The deformation would not result in a good fit of the assembled parts and

would thus lead to a failure. Mismatch of the components during the assembly is also an

important cause for concern. The other major factors affecting the safety are the changes in

the manufacturing tolerances for the components, road hazards, corrosion of the

component materials and the tires. The safe operation of the tires play an important role in

reducing the danger associated with the rims. The process of mounting a tire onto a rim is a

very crucial process. It could lead to a potentially life threatening situation. The improper

inflation and also the deflation of the tires also affect the safety of the rims. The multi-

piece rims are essentially a concentric fit of two interlocking parts. If any of them are not

4

in the precise location of the designer’s intent when the rim and the tire assembly is

inflated, it may result in a separation of the rim components.

The present work concentrates more on the stress and concentric displacement analysis of

the two-piece rim components in use.

1.3 OBJECTIVE

Multi-piece wheels or rims used on large vehicles such as trucks, tractors, trailers, buses

and off-road machines have often been known for their dangerous properties. This is

because of the large number of catastrophic accidents that they have been involved in. The

accidents have in most cases resulted in serious injury or even death to the workers. The

main problem with these types of rims is when the tire is mounted or demounted from the

rim, the assembly blows off. The cause of the actual blow off varies from mismatch of the

parts during the assembly, wear of the components and improper design. Numerous

product liability lawsuits have been put up seeking compensation for the damages and the

complete removal of these rims from the market. Though there has been a strong demand

for a ban on the multi-piece rims, the wheel industry was successful in avoiding it by

supporting an awareness and educational program brought out by the Occupational Safety

and Health Administration (OSHA). The OSHA introduced a guideline in 1980 for

servicing multi-piece and single rims. This guideline contains the servicing equipment that

is recommended and the training that is required by the employee to work on the rims. It

was also made mandatory to display this guideline in all the tire service stations and other

places where the rims are assembled, mounted or demounted. The net result of this entire

educational program was transfer of the liability from the manufacturer to the employees

working on the rims.

5

Although OSHA guidelines require, among other things, the use of a safety cage during

the tire mounting operation, accidents still occur after the wheel is removed from the safety

cage, for example, when it explodes as it is being mounted on the vehicle. The warnings

(which are part of the educational program) are not an adequate substitute for a safer

design.

The present work seeks to analyze a two-piece rim similar to those manufactured by some

of the most prominent rim manufacturers in the USA. The actual rim being analyzed is the

7.5 Type FL Rim, 2 Pc Design, Non-Demountable with and without valve hole. A linear

static stress and deformation analysis would be performed to look into the areas of

maximum stress development and also the areas of maximum deformation. Non-linear

effects will not be considered in this investigation. Reliability of the rims and the effect of

regulations enforced on the rims such as the Occupational Health and Safety (OSHA)

guideline will be reviewed.

6

CHAPTER TWO

REVIEW OF PUBLISHED LITERATURE

2.1 BACKGROUND

The modern day truck wheel has undergone many changes in design to improve its overall

performance on the road. Most of the earlier work on the analysis of tire rims was

undertaken during the 1970s and 1980s. Bradley [1] traces the development of the modern

truck disc wheel from the World War II times. Initially the flat base rim was the standard

of the industry before 1945. In 1945 two types of rims- the advanced rim and the interim

rim were introduced. The interim rim had a new side ring to the original flat base. This

gave the tire additional support. The advanced rim was a three piece rim, side ring and lock

ring combination. It had more advantages than the interim rim design. Bradley also

discusses the development of the disc portion of the wheel, the tubed and the tubeless

wheel assemblies. The bevel weld construction of the disc for weight reduction in tubed

wheel assemblies is shown. The introduction of the drop centre single piece rim for

tubeless tires was also discussed. The development of the duo rim has also been traced and

its design features were clearly described. The duo rim could function both as a tubed or a

tubeless rim.

2.2 STRESS ANALYSIS

Ridha [2] presented a finite element stress analysis of automotive wheels which could be

applied not only to the rim but to the entire wheel. The rim cross-section was first modeled

by an interconnected grid of fine triangular elements. The displacements of each element

were calculated and then the strains and finally the stress distribution obtained. The

formulation of the stiffness matrix of a constant strain triangular element for axisymmetric

7

problems was given along with the modifications for non-axisymmetric problems. He

concluded from the analysis that the largest principle stresses were located in the regions

of sharp changes in the rim’s contour, i.e., the flanges and the drop centre. He also

discussed the effects of increasing the width of the rim for reducing the stress levels.

Morita et al [3] showed that the present FEM stress evaluation technique was a good and

effective way to develop new designs for wheels. The induced stress of the wheel in the

rotating bending fatigue test was simulated by a three dimensional finite element analysis

of the wheel. The stress distribution was obtained and the results were compared to

experimental results from strain gauges on a wheel. The comparison yielded similar results

from both of them. The wheel that they had analyzed was a passenger car wheel (5-1/2 JJ x

14 WDC). The element used for the FEM modeling was a four-node iso-parametric shell

element. The effect of different design parameters like the disc thickness, disc hat radius

and rim thickness were also studied numerically. All the three parameters had an inverse

proportional relation with the stress amplitude.

Stearns [4] investigated the effects of tire air pressure along with the radial load on the

stress and displacement of aluminum alloy tire rims in his doctoral dissertation. The effects

of providing an opening on the rim and also environmental degradation were also

investigated. ALGOR was used in the modeling and analysis of the rim, which was a

single piece type. Stearns’ research revealed that the finite element analysis of the rim was

more accurate with a brick element rather than a shell or a plate element. Critical areas

were identified both on the rim and the disc. The Von Mises stresses in the disc were

found to be much lower than that in the rim. The inboard bead seat area was identified to

be the area of maximum stress. The stress was however below the endurance limit for the

applied loading condition. The effect of providing a square opening resulted in 10% higher

stress concentration when compared to a round hole opening at the same location.

8

Ridder et al [5] looked into the incorporation of reliability theory into a fatigue analysis

algorithm. A design algorithm had been developed and the automotive wheel assembly

was taken as an example to demonstrate its application. Using the program, failure vs.

cycles curves had been developed for different alloys like 1010 Steel, DP Steel and 5454

Aluminum. The effects of driver and route variations and also material processing effects

have been studied. Based on the information collected and the results from the analysis, the

most reliable wheel spider of the three alloys in consideration was suggested. The effects

of fatigue crack growth on durability have not been dealt with. This case study was

concentrated only on component reliability for determination of the best possible material

for the job.

The safety and salient features of both single and multi-piece rim types in the context of

field performance were discussed by Watkins and Blate [6]. The failure of multi-piece rims

was discussed with a theoretical approach. They had reviewed different finite element

analyses discussed above to verify adequacy of the existing design. Results of multi-piece

component analysis had not been presented. Statistical analysis of accident data had also

been performed. The OSHA guideline on servicing different types of rims had come out

only a year earlier and the authors expected the injuries to be minimized as a result of it.

The literature review reveals that most of the analysis and studies on rims had not clearly

addressed the problem of failure of multi-piece rims and the huge accident data associated

with them. The OSHA guideline was expected to minimize or control the number of

accidents relating to multi-piece rims. The effect of OSHA standard on the actual

serviceability would be revealed by a complete statistical analysis of the data after its

implementation. This review provides a clear direction to the present study.

9

CHAPTER THREE

FINITE ELEMENT ANALYSIS

3.1 INTRODUCTION TO FEA

The finite element method is a numerical method for solving problems of engineering and

mathematical physics. Typical problem areas of interest in engineering and mathematical

physics that are solvable by the use of the finite element method include structural analysis,

heat transfer, fluid flow, mass transport, and electromagnetic potential. This method is

used to solve complex problems that are difficult to be satisfactorily solved by other

analytical methods. It actually originated as a method of analyzing the stress distribution in

different systems.

The concept of Finite Element Analysis was initially proposed by Courant in 1941 [7]. In a

work published in 1943, he used the principle of stationary potential energy and piecewise

polynomial interpolation over triangular sub regions to study the Saint-Venant torsion

problem. Approximately ten years later engineers had set up stiffness matrices and solved

the equations with the help of digital computers. The exact behavior of a structure at any

point can be approximated by using the numerical solutions at discrete points, called nodes.

The nodes are connected by the elements. The approximate solution for each element is

represented by a continuous function, which leads to a system of algebraic equations. The

complete solution is then generated by assembling the elemental solutions, allowing for the

continuity at the inter-elemental boundaries.

There are numerous element types that could be chosen for a given structure. The selection

of the appropriate element type depends on the problem at hand. An element or mesh that

10

works fine in a particular situation may not be as good for a different situation. The

engineer should select the best element for a problem understanding well both the nature of

the element behavior and the problem itself. The numerical hand calculations using this

method become increasingly difficult with the complexity in the geometry of the structure

and with increasing number of nodes. For this reason, several finite element computer

programs have been developed by research organizations that can produce reliable

approximate solutions, at a small fraction of the cost of more rigorous, closed-form

analyses.

Out of all the numerous computer programs currently available to analyze finite element

problems, ANSYS is very popular software. ANSYS can be efficiently used to analyze a

number of models in most of the above mentioned areas in engineering and mathematical

physics.

3.2 INTRODUCTION TO ANSYS

ANSYS Inc developed and maintains ANSYS, a general purpose finite element modeling

package for numerically solving static/dynamic structural analysis (both linear and non-

linear), fluid and heat transfer problems as well as electromagnetic and acoustic problems.

From the available element library in ANSYS, the element used for modeling the rim

section is the SOLID95 type. SOLID95 is a higher order version of the 3-D 8-node solid

element SOLID45 [8]. It can tolerate irregular shapes without as much loss of accuracy.

SOLID95 elements have compatible displacement shapes and are well suited to model

curved boundaries. The element is defined by 20 nodes having three degrees of freedom

per node: translations in the nodal x, y, and z directions. The element may have any spatial

11

orientation. Elements are generated using free/mapped/automatic meshing. The

convergence of results is ensured by refining mesh size (increasing the number of

elements) i.e. h-FEA is adopted. The p-method is more tolerant for element

distortion and geometry quality such as aspect ratio, skew ness angle etc. Also the

number of elements is much less compared to h-method; hence no mesh refinement

is needed for complicated geometry.

Figure 3.1: SOLID95 3-D 20-Node Structural Solid

(Courtesy: ANSYS, Inc. Theory Reference)

12

3.3 INTRODUCTION TO PRO/E

Solid modeling, as a field is the result of several convergent developments like automated

drafting systems, free-form surface design and graphics and animation. The incorporation

of component design intent in a graphical model by means of parameters, relationships and

references is known as the parametric design. Pro/E is one of the most widely used

parametric solid modeling software available today. It can be efficiently used for modeling

complex parts, features and assemblies. The wheel rim is one such complex component

which can be easily modeled using Pro/E.

3.4 MODELING USING PRO/E

The two-piece rim used for the analysis is modeled using Pro/E. The rim as already

discussed contains two parts- the rim base and the side ring. The two-piece design is a

concentric fit of these two combining parts. First, the rim base is modeled as a part using

the ‘revolve’ option in Pro/E. Then, the side ring is also modeled as a part. The two parts

are then assembled using the ‘components assemble’ option. The assembly is checked for

the accurate fit of the two parts in the proper designated location. The two-piece rim is

modeled as a 3600 solid as shown in the figure 3.2. But due to the symmetry in the

geometry, a 20 model is used for the analysis.

13

Figure 3.2: Tube-Type Demountable Rim Assembly (two-piece)

14

Figure 3.3: Rim Base

Figure 3.4: Split Side Ring

15

3.5 ANALYSIS OF TWO-PIECE RIM

The 20 rim modeled in Pro/E is saved as a .iges file. It is then imported into ANSYS using

the import file command. The import file command in ANSYS can import models from

Pro/E in the .iges file mode.

The element type used for the model is chosen as SOLID 95 from ANSYS element menu.

Previous research [4] has shown that the solid element is a better option to model the

wheel and rim components than the shell elements. The model is then assigned the

material properties like Young’s Modulus, Poisson’s ratio and density of steel. The

meshing is done with the ‘mesh tool’ option in ANSYS. A free tetragonal mesh for

volumes is generated. The total number of elements created as a result of the meshing

process is 22896. Then the loading and the boundary conditions are applied to the model.

The model is restrained in all degrees of freedom (ALL DOF) on the lower left side region

of the rim base. This is the area where the disc or the spokes are attached or bolted to the

rim connecting it to the hub. Since the 20 model is used due to symmetry, the symmetry

boundary conditions are applied to the side edges of each component in the two-piece

assembly. A pressure loading of 90 psi is applied to the top cup surface of the model. This

is the inflation pressure of the tire acting on the top surface of the rim.

16

Figure 3.5: Two degree model of rim imported into ANSYS

Figure 3.6: Elements generated using the meshing option in ANSYS

17

3.6 RESULTS AND DISCUSSION

The model is run for the applied boundary and loading conditions. Due to the complexity

of the assembly model and the total number of the elements involved, the processing time

is very high. The model solves for an approximate time of around two hours. The general

post processing of the model yielded the deformation and the stress results. A result

summary from the General post processing menu gave the overview of all the required

results. The deformed shape of the rim assembly as a result of the pressure loading is

shown below from the ANSYS plot, figure 3.7. Also, a plot of the deformed and the un-

deformed shape of the assembly is shown in figure 3.8.

Figure 3.7: ANSYS plot of the deformed shape of the rim assembly.

18

Figure 3.8: ANSYS plot of the deformed and un-deformed shape of the rim assembly.

Figure 3.9: ANSYS plot of the Von-Mises stress profile of the rim assembly.

19

From the plots it is very clear that the assembly comes apart due to the inflation pressures

of the tire on the rim. The figure 3.7 shows that the side ring is dislocated by 0.00375

inches. The tongue-in-groove principle of locking the two components, as the fit is usually

referred to as, has the greatest challenge of retaining the side ring in the groove when the

extreme pressure acts on the assembly. Roughly half the inflation pressures act on the side

ring, imposing on it a very high force to move out of the groove. The axisymmetric

inflation pressure acting on the rim produces an axial force on the side ring and also

induces shearing and bending effects. The axial force causes the side ring to move in the

‘x’ direction and the bending moment causes it to dislocate from the original designer

intent position. Also, the tire bead runs through the area of dislocation. The weakening of

the tire bead, made up of drawn steel cables which carries most of the hoop stress further

adds to the impulsive force against the side ring causing it to fail. The outward directed

axial force acting on the side ring due to the pressure of inflation is very high and pushes

the ring in the direction of the force acting. The plots from ANSYS are indicative of the

type of dislocation that is expected due to the forces acting as a result of the inflation

pressure.

The effect of changing the position of the side ring along the circumference of the rim base

does not help the situation any further. The simulation run in ANSYS was done changing

the position of the side ring, i.e., the dislocated area of the side ring is placed in a new

position on the rim base and similar results have been obtained. The stress contour plot

shows that the maximum stresses occur in the region of contact between the two

components and the bead seat area. But due to the high stress acting on the side flange, a

little deformation is observed on the base area which is in contact with the other

component and through which runs the tire bead.

20

The results from the ANSYS simulation were checked with some actual rim failure pieces.

The dislocation is very similar to the one that is obtained from the simulation. The ring or

the flange is moved out of the position of intent. Figure 3.10 shows the original position of

a side ring when the components are fit exactly. Figure 3.11 shows the rim components

from a failure case. Clearly the movement of the ring off the base area is replicated from

the ANSYS results shown in figure 3.13 and figure 3.14. The effect of changing the

position of the area of dislocation was also done on the actual components and found to be

not successful.

Figure 3.10: Original fit of the components in a multi-piece rim.

21

The figure above shows the original fit of the components in a multi-piece rim. The black

portion of the picture is the side ring which is in exact concentric fit with the rim base,

which is the brown portion of the picture. The side ring is snapped onto the rim base to

form the exact fit. The figures 3.11 and 3.12 show the fit from a multi-piece rim whose

side ring is dislocated from its original position. This is because of the effect of inflation

pressures and other forces acting on it during its operation.

Figure 3.11: Dislocation of the ring portion from the rim base at position 1.

22

Figure 3.12: Rotational dislocation of ring portion from rim base at position 2.

23

Figure 3.13: Separation of the side ring from the rim base from ANSYS simulation.

Figure 3.14: Dislocation of side ring from rim base from ANSYS simulation.

24

CHAPTER FOUR

RELIABILITY ANALYSIS

The term ‘Reliability’ is defined as the probability that a product or component can

perform its desired function for a specified interval under stated conditions. The need for

the reliability analysis of different components is important because of the demands for

their safer operation. The data from the failures of components is initially organized into

distributions and then analyzed for their failure rates, safety index etc.

4.1 STATISTICAL DISTRIBUTIONS

A reliability function and its related hazard function are unique. Each reliability function

has a single hazard function and vice versa. All the failure related data can be fit into some

of the common failure density functions, each having its related hazard function. Some of

the most common among them are briefly discussed here.

4.1.1 Exponential Distribution:

The exponential distribution is widely used in reliability. The probability density function

for an exponentially distributed random variable ‘t’ is given by

f(t)=(1/θ) e-t/θ , t 0≥

where θ is a parameter called the mean of the distribution, such that θ>0, and

R(t) = e θt−

, t 0≥

4.1.2 Log Normal Distribution:

The log normal density function is given by

f(t)=πσ 2

1t

exp⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −

−2ln2/1

σµt

, t 0≥

where µ and σ are parameters such that -∞ < ∞<µ and 0>σ .

25

4.1.3 Weibull Distribution:

The cumulative distribution for a random variable, x, distributed as the three-parameter

Weibull is given by,

,1),,;()( β

δθδ

δβθ −−

−−=

x

exF δ≥x

where 0,0 >> θβ and 0≥δ . The parameter β is called the shape parameter or the

Weibull slope, θ is the scale parameter or the characteristic life and δ is called the

location parameter or the minimum life. The scale parameter is also sometimes indicated

by η. The two-parameter Weibull has a minimum life of zero and the cumulative

distribution is given by,

,1),;()( β

θβθx

exF−

−= 0≥x

The three-parameter Weibull can be converted into the two-parameter distribution by a

simple linear transformation. The Weibull probability density function for the two-

parameter distribution is given as

β

θβ

θθββθ

)(1)(),;(x

exxf−−= , 0≥x

The hazard function is given by

,)()( 1−= β

θθβ xxh 0≥x

The hazard function is decreasing when 1<β , increasing when β >1, and constant when

β is exactly 1. The hazard function h(x) will change over the lifetime of a population of

products somewhat as shown in the figure below. The first interval of time represents early

failures due to material or manufacturing defects. Quality control and initial product

testing usually eliminate many substandard devices, and thus avoid this initial failure rate.

Actuarial statisticians call this phase of the curve “infant mortality”. The second phase of

26

the curve represents chance failures caused by the sudden stresses, extreme conditions, etc.

In actuarial terms this could be equated to the accidents encountered by the population of

individuals on a day-to-day basis. The portion of the curve beyond this region represents

wear out failures. Here the hazard rate increases as equipment deteriorates.

4.2 GOODNESS-OF-FIT TESTS

The failure data which is modeled into different distributions can be tested for the best fit

distribution using a couple of methods. These are the Anderson Darling Test and the

Goodness-of-fit test for a statistical distribution.

The Anderson-Darling test [9] is used to test if a sample of data came from a population

with a specific distribution. It is a modification of the Kolmogorov-Smirnov (K-S) test and

gives more weight to the tails than does the K-S test. The K-S test is distribution free in the

sense that the critical values do not depend on the specific distribution being tested. The

Anderson-Darling test makes use of the specific distribution in calculating critical values.

This has the advantage of allowing a more sensitive test and the disadvantage that critical

values must be calculated for each distribution. Currently, tables of critical values are

available for the normal, lognormal, exponential, Weibull, extreme value type and logistic

distributions. This test is usually applied with a statistical software program that will print

27

the relevant critical values. The Anderson-Darling test is an alternative to the chi-square

and K-S goodness-of-fit tests.

The Anderson-Darling test statistic is defined as

SNA −−=2

where ))](1ln()()[ln12( 11

iNi

N

iYFYF

NiS −+

=

−+−

= ∑

‘F’ is the cumulative distribution function of the specified distribution and are the

ordered data.

iY

The critical values for the Anderson-Darling test are dependent on the specific distribution

that is being tested. Tabulated values and formulas have been published [8] for a few

specific distributions (normal, lognormal, exponential, Weibull, logistic, extreme value

type 1). The test is a one-sided test and the hypothesis that the distribution is of a specific

form is rejected if the test statistic, A, is greater than the critical value.

The second method for testing the goodness-of-fit is the Correlation Coefficient method.

The correlation coefficient, r2 (sometimes also denoted as R2) is a quantity that gives the

quality of a least squares fitting to the original data. It is defined by

∑ ∑ ∑ ∑

∑ ∑ ∑−−

−=

])(][)([ 2222 yynxxn

yxxynr

or can be stated in more simpler terms as yyxx

xy

SSSSSS

r2

2 =

where are the sum of squared values of a set of ‘n’ data points

about their respective means. The correlation coefficient is also known as the product-

moment coefficient of correlation or Pearson’s correlation. The value of the maximum

correlation coefficient for a set of failure data modeled using different distributions could

be reasonably assumed to be the best fit distribution.

xyyyxx SSSSSS ,, ),( ii yx

28

4.3 FAILURE DATA OF DIFFERENT TYPES OF RIMS

The large numbers of multi-piece rim accidents occurring over the last few decades have

resulted in a number of product liability lawsuits being filed. The main objectives of these

lawsuits were to seek the removal of the multi-piece tire rims from operation and to

demand compensation for the accidents. The present set of data pertaining to the record of

these wheel rim accidents has been produced by all the major rim manufacturers to The

Circuit Court of Kanawha County, West Virginia, in relation to a lawsuit. The data was

turned in as an exhibit in the Civil Action No. 88-C-1374 [10]. Each data file had the name

of the victim and the date, time and place the accident had taken place. It also specified the

type of rim causing the accident and the manufacturer in most cases. The resulting injury

to the victim and the plaintiffs on behalf of the victim were also included in the details

pertaining to each lawsuit. The total number of accident cases that were investigated in this

study is 985. The time period involving the data was from 1955 to 1987.

The huge number of accidents involving the multi-piece wheel rims caused a lot of

concern to the Occupational Health and Safety Administration (OSHA). OSHA is an

organization of the U.S Department of Labor whose goal is to assure the safety and health

of America's workers by setting and enforcing standards and encouraging continual

improvement in workplace safety and health. OSHA initially sought to ban all the multi-

piece rims but could not do so because of pressure from the wheel industry. Hence, they

had brought out a standard for servicing multi-piece and single piece rim wheels in 1980

[11]. This was part of an educational program to increase the awareness among tire

mounters and workers in the service stations.

The data has been thoroughly reviewed and organized into two sets. The first set of data

contains the details of accidents before the OSHA guideline had come into effect and the

second set of data contains the details of accidents after the guideline was enforced. A

tabular format containing the number of various types of wheel rim accidents and the year

29

of the accident for each set of data was created. The tabulated data has been first plotted

for the accident curves with respect to the year of accident.

The summary of the number of cases is given below.

Total Number of Accident Cases Listed: 985.

Number of ‘RH 5o’ rim accidents: 411.

Number of Two Piece rim accidents: 147.

Number of Three Piece rim accidents: 43.

Number of Single Piece rim accidents: 44.

Number of Unknown rim type accidents: 340.

RH 5 Rim Two Piece

Rim Three

Piece Rim Unknown Year Accidents Accidents Accidents Accidents 1955 1 1956 1957 1958 1959 1 1960 2 1961 2 1962 1 1963 1964 1 1965 4 1966 2 1 1967 4 1968 4 2 1 1969 11 1970 10 4 1971 11 5 8 1972 10 1 13 1973 16 3 27 1974 16 4 4 10 1975 16 4 2 10 1976 11 3 3 9 1977 23 8 2 22 1978 24 10 5 27 1979 23 11 6 34

Table 4.1: Accident statistics for different types of rims before OSHA Guideline

30

RH 5 Rim

Two Piece Rim

Three Piece Rim Unknown

Year Accidents Accidents Accidents Accidents 1980 22 11 1 26 1981 46 9 2 36 1982 28 16 5 15 1983 29 17 5 21 1984 32 10 4 24 1985 19 10 2 15 1986 15 8 9 1987 19 9 1 5

Table 4.2: Accident statistics for different types of rims after OSHA Guideline

Single Piece Year Accidents 1969 2 1970 1971 1 1972 1 1973 1974 4 1975 2 1976 5 1977 4 1978 3 1979 2

Table 4.3: Accident statistics for single-piece rims before OSHA Guideline

31

Single Piece Year Accidents 1980 5 1981 5 1982 4 1983 1984 4 1985 1 1986 1 1987

Table 4.4: Accident statistics for single-piece rims after OSHA Guideline

From the above data set, the failures relating to only the steel component failure are taken

into consideration for the purpose of this investigation. The rubber failures like the tire

blow-out during inflation or deflation, tire bead failures are eliminated. This is because the

present investigation only deals with failure of rim components, i.e. steel components. The

failure due to rubber is not considered here. Among the single-piece failures, the different

modes of failure were found out to be failure during mounting, failure during assembly,

moving vehicle incidents and separation during welding. From the above modes, only the

separation during welding is considered as a steel component failure and the rest are

determined to be rubber failures. Hence, looking into the separation due to welding failures

in the single-piece rim data, only 1 failure was found. Thus this failure data is used for the

single-piece rim analysis.

Single Piece Year Accidents 1985 1

Table 4.5: Accident statistics for single-piece rims (non-rubber failures).

32

Accident curves for different types of rims

05

101520253035404550

1950 1960 1970 1980 1990

Year of Accidents

Num

ber o

f Acc

iden

ts

RH 5 rims

Two Piece rims

Three Piece rims

Single Piece rims

Unknown rims

Figure 4.1: Graph for all the different types of rim accidents.

RH 5 degree rims

0

10

20

30

40

50

1970 1975 1980 1985 1990

Year of Accidents

Num

ber o

f Acc

iden

ts

Pre OSHA Standard

Post OSHA Standard

Figure 4.2: Accident Curves for RH 5 rims.

33

Two-piece rims

0

5

10

15

20

1970 1975 1980 1985 1990

Year of Accidents

Num

ber o

f Acc

iden

ts

Pre OSHA StandardPost OSHA Standard

Figure 4.3: Accident Curves for Two Piece rims.

Three-piece rims

01234567

1970 1975 1980 1985 1990

Year of Accidents

Num

ber o

f Acc

iden

ts


Figure 4.4: Accident Curves for Three Piece rims.

34

Accident curves for single-piece rims

0

0.2

0.4

0.6

0.8

1

1.2

1970 1972 1974 1976 1978 1980 1982 1984 1986 1988

Year of Accidents

Num

ber o

f Acc

iden

ts


Figure 4.5: Accident Curves for Single Piece rims.

Accident curves for unknown rim types

05

10152025303540

1970 1975 1980 1985 1990

Year of Accidents

Num

ber o

f Acc

iden

ts


Figure 4.6: Accident Curves for Unknown type rims.

The above graphs are a simple representation of the failure data of the different rims.

These graphs show that in most cases the accident curves have risen after the OSHA

standard was introduced. This is particularly evident from the RH 5 degree and the two-

piece rim curves.

35

4.4 ANALYSIS OF DATA USING MINITAB

The above failure data for different types of rims is analyzed using the statistical analysis

software MINITAB 14. MINITAB is widely used software developed by MINITAB Inc. It

can be used for various purposes like Statistical Process Control, Time Series and

Forecasting, Reliability/Survival Analysis, Design of Experiments etc. [12]. Data is

imported into a Minitab Project file from an Excel sheet using the options from the

Minitab Software. The data is then re-grouped according to the types of rims and the year

of consideration, i.e. the year in which OSHA introduced the guideline for servicing the

multi-piece rims.

The data is first modeled into different distributions using MINITAB. Some of the

distributions used were the 2 parameter Weibull, 3 parameter Weibull, exponential, normal,

log-normal, log-logistic etc. After modeling the data, a best fit test was run. The tests used

for determining the best fit were the Anderson-Darling test and the Correlation Coefficient

method. For the Anderson-Darling test, the test statistic value should be the least in order

for the data to best fit the distribution. The values of the computed Anderson-Darling test

statistic for different rim data shows that the value for the 3 parameter Weibull is the least

in most of the cases. The correlation coefficient value should be the highest, for a data to

best fit the distribution. From this method also, it is sufficiently proved that the 3

parameter Weibull is the best fit distribution. The 3 parameter Weibull is widely known as

the best fit distribution to model the failure data in most of the engineering situations. The

values from the MINITAB analysis for the goodness-of-fit tests are given in the appendix.

Weibull distribution analysis is performed on the data. That is because mechanical

products tend to degrade over a period of time and are more likely to follow a distribution

with a strictly increasing hazard function. The Weibull distribution is a generalization of

the exponential distribution that is appropriate for modeling lifetimes that have constant,

increasing and decreasing hazard functions. A 95% confidence interval is chosen for the

36

Weibull analysis. The shape (β), the scale (θ) and the location (δ) parameters from the

analysis of each set of data are investigated with greater detail.

The single-piece rim data used for the analysis is obtained from the Table 4.5. There is

only one failure case that is appropriate to the present investigation. This data is

insufficient for the analysis in MINITAB. It is difficult to perform a distributional analysis

on a single point. Hence, the MINITAB plots for the single-piece rim data are not shown

below.

37

RH 5 degree rim accident data analysis

Pre OSHA (Years)

PDF

12840

0.15

0.10

0.05

0.00

Pre OSHA (Years) - Threshold

Perc

ent

101

99.9

90

50

10

1

0.1

Pre OSHA (Years)

Perc

ent

12840

100

50

0

Pre OSHA (Years)

Rat

e

12840

1.0

0.5

0.0

Table of Statistics

StDev 2.34280Median 4.85375IQ R 3.28268Failure 139C ensor 0

Shape

A D* 3.904C orrelation 0.965

2.48589Scale 6.14035Thres -0.444858Mean 5.00251

Probability Density Function

Survival Function Hazard Function

RH 5 degree rims (Pre OSHA Standard)LSXY Estimates-Complete Data

3-Parameter Weibull

Figure 4.7: Distribution overview plot for RH 5 rim accident data (Pre OSHA Standard).

Post OSHA (Years)

PD

F

1050

0.2

0.1

0.0

Post OSHA (Years) - T hreshold

Pe

rce

nt

10.01.00.1

99.9

90

50

10

1

0.1

Post OSHA (Years)

Pe

rce

nt

1050

100

50

0

Post OSHA (Years)

Ra

te

1050

0.75

0.50

0.25

0.00

Table of Statistics


Shape


1.72750Scale 3.94192Thres 0.441409Mean 3.95489


Surv iv al F unction Hazard Function

RH 5 degree rims (Post OSHA Standard)LSXY Estimates-Complete Data

3-Parameter Weibull

Figure 4.8: Distribution overview plot for RH 5 rim accident data (Post OSHA Standard).

Distribution Overview plot is hereafter referred to as D.O plot.

38

Two-piece rim accident data analysis

Pre OSHA (Year)

PD

F

1050

0.20

0.15

0.10

0.05

0.00

Pre OSHA (Year) - T hreshold

Pe

rce

nt

201510

90

50

10

1

Pre OSHA (Year)

Pe

rce

nt

1050

100

75

50

25

0

Pre OSHA (Year)

Ra

te

1050

2.0

1.5

1.0

0.5

0.0

Table of Statistics


Shape


8.89550Scale 16.3643Thres -9.69207Mean 5.79615



Two-piece rims (Pre OSHA Standard)LSXY Estimates-Complete Data

3-Parameter Weibull

Figure 4.9: D.O plot for two-piece rim accident data (Pre OSHA Standard).

Post OSHA (Year)

PDF

1050

0.15

0.10

0.05

0.00

Post OSHA (Year) - Threshold

Perc

ent

10.01.00.1

99.9

90

50

10

1

0.1

Post OSHA (Year)

Perc

ent

1050

100

50

0

Post OSHA (Year)

Rat

e

1050

1.2

0.8

0.4

0.0

Table of Statistics


Shape


2.33256Scale 5.13653Thres -0.340631Mean 4.21070



Two-piece rims (Post OSHA Standard)LSXY Estimates-Complete Data

3-Parameter Weibull

Figure 4.10: D.O plot for two-piece rim accident data (Post OSHA Standard).

39

Three-piece rim accident data analysis

Pre OSHA (Year)

PD

F

1050

0.20

0.15

0.10

0.05

Pre OSHA (Year) - T hreshold

Pe

rce

nt

105

90

50

10

1

Pre OSHA (Year)

Pe

rce

nt

1050

100

50

0

Pre OSHA (Year)

Ra

te

1050

2

1

0

Table of Statistics


Shape


5.24144Scale 9.31539Thres -2.70130Mean 5.87506


Surv iv al Function Hazard Function

Three-piece rims (Pre OSHA Standard)LSXY Estimates-Complete Data

3-Parameter Weibull

Figure 4.11: D.O plot for three-piece rim accident data (Pre OSHA Standard).

Post OSHA (Year)

PDF

7.55.02.50.0

0.2

0.1

0.0

Post OSHA (Year) - Threshold

Perc

ent

52

90

50

10

1

Post OSHA (Year)

Perc

ent

7.55.02.50.0

100

50

0

Post OSHA (Year)

Rat

e

7.55.02.50.0

1.5

1.0

0.5

0.0

Table of Statistics


Shape


3.21665Scale 5.23958Thres -0.702802Mean 3.99124



Three-piece rims (Post OSHA Standard)LSXY Estimates-Complete Data

3-Parameter Weibull

Figure 4.12: D.O plot for three-piece rim accident data (Post OSHA Standard).

40

Unknown rim type accident data analysis

Pre OSHA (Years)

PD

F

12840

0.15

0.10

0.05

0.00

Pre OSHA (Years) - T hreshold

Pe

rce

nt

10.01.00.1

99.9

90

50

10

1

0.1

Pre OSHA (Years)

Pe

rce

nt

12840

100

50

0

Pre OSHA (Years)

Ra

te

12840

0.6

0.4

0.2

0.0

Table of Statistics


Shape


1.77887Scale 5.36684Thres 0.282511Mean 5.05801



Unknown rims (Pre OSHA Standard)LSXY Estimates-Complete Data

3-Parameter Weibull

Figure 4.13: D.O plot for unknown rim accident data (Pre OSHA Standard).

Post OSHA (Years)

PD

F

7.55.02.50.0

0.2

0.1

0.0

Post OSHA (Years) - T hreshold

Pe

rce

nt

10.01.00.1

99.9

90

50

10

1

0.1

Post OSHA (Years)

Pe

rce

nt

7.55.02.50.0

100

50

0

Post OSHA (Years)

Ra

te

7.55.02.50.0

0.75

0.50

0.25

0.00

Table of Statistics


Shape


1.63522Scale 3.39515Thres 0.429022Mean 3.46723

Probability Density F unction


Unknown rims (Post OSHA Standard)LSXY Estimates-Complete Data

3-Parameter Weibull

Figure 4.14: D.O plot for unknown rim accident data (Post OSHA Standard).

41

4.5 RESULTS AND DISCUSSION

The Weibull analysis from MINITAB yields the shape and scale parameter for fitting the

particular data into a distribution. From the above analysis, we can state the results as

follows:

Type of rim: RH 5o

Time period

Shape Parameter

Scale Parameter

Pre OSHA Standard (1972-

1979)

2.485

6.14

Post OSHA Guideline (1980-

1987)

1.727

3.941

Table 4.6: Results from analysis of ‘RH 50’ type rim data using MINITAB.

Type of rim: Two piece

Time period

Shape Parameter

Scale Parameter


1979)

8.895

16.364

Post OSHA Standard (1980-

1987)

2.332

5.136

Table 4.7: Results from analysis of two-piece type rim data using MINITAB.

42

Type of rim: Three piece

Time period

Shape Parameter

Scale Parameter


1979)

5.241

9.315


1987)

3.216

5.239

Table 4.8: Results from analysis of three-piece type rim data using MINITAB.

Type of rim: Unknown

Time period

Shape Parameter

Scale Parameter


1979)

1.778

5.366


1987)

1.635

3.395

Table 4.9: Results from analysis of unknown type rim data using MINITAB.

43

From the above results it is clear that the shape parameter, β, is greater than 1 in all the

cases. This indicates that the hazard function of the rim failures is an increasing function

and the data do not represent an early-life or commissioning failures. The shape parameter,

as the name implies, determines the shape of the distribution. When β is greater than 1, we

can reasonably approximate the data to be characteristic of increasing failure rate or hazard

function. In the case of RH 5o type rims, the shape parameter changed from 2.485 in the

time period before the OSHA guideline to 1.727 after the OSHA guideline. This implies

that the failure data distribution has changed from being approximately log-normal before

the guideline to somewhere in between exponential and log-normal distribution after the

guideline. The β values for two-piece rim data have changed from 8.895 before the

guideline to 2.332 after the guideline. The value of β for three-piece rim data before the

OSHA guideline was 5.241. The β value for three-piece rims after the OSHA guideline

had been introduced was obtained as 3.216. This implies that the distribution has an

increasing hazard function and could be fairly approximated to be a normal distribution.

The results for the single-piece rim data indicate that β changed from being 7.448 during

the time when the OSHA guideline was not existent to 1.37 after 1980. Similarly, the β

values for the unknown rim type data also changed from 1.778 before 1980 to 1.635 after

1980.

The distribution used for the analysis here is the 3 parameter Weibull distribution. The

failure rate for a 3 parameter Weibull distribution is calculated by the following formula:

1)(. −

−−

−= β

δηδ

δηβ tRF

η here is the scale parameter which is also sometimes indicated by θ.

Using the above formula, calculations were made for the failure rates of different types of

rims. The results at the end of the time period of 8 years for each set of data are tabulated

below.

44

Type of rim

Failure Rate

(Pre-OSHA Standard)

Failure Rate

(Post-OSHA Standard)

RH 5 degree rim

0.546289

0.863966

Two-piece rim

0.01606

0.745866

Three-piece rim

0.266757

1.261069

Unknown rims

0.484256

0.999762

Table 4.10: Failure Rates of different types of rims before and after the OSHA Standard.

From the table shown above it is very clearly evident that the failure rates of the different

rim types have increased after the OSHA Standard had come into effect. The failure rates

in the case of two-piece, three-piece and single-piece rims show a drastic increase from

before the standard to after its introduction. There has also been considerable increase in

the failure rates of RH 5 degree rims and unknown rims. This shows that there had been

very little effect of the standard on the number of accidents involving the multi-piece rims.

The beta values which are indicative of the slope of the curve for the data are very high.

The beta values of some of the rim types have been compared with other published data of

different engineering systems and components. Table 4.11 shows the low, typical and high

beta values for these components. The results of the rim data when compared to these other

components clearly fall on the higher side, which is not very desirable. The beta values

45

should be reduced, so that the failure or hazard associated with them also decreases. The

beta values can only be reduced with better efforts to maintain the rims and control the

number of accidents.

Item Beta Values (Weibull Shape Factor)

Low Typical High

Nuts 0.5 1.1 1.4

Pumps, lubricators

0.5 1.1 1.4

Vibration mounts

0.5 1.1 2.2

Compressors, centrifugal

0.5 1.9 3

Steam turbines

0.5 1.7 3

Gears 0.5 2 6

Two-piece rims

8.8

Three-piece rims

5.2

Table 4.11: Beta values comparison of multi-piece rims with different engineering

components.

46

CHAPTER FIVE

CONCLUSIONS

5.1 SUMMARY

The desired objective of looking into the rotational dislocation of the multi-piece rim

components has been established and also the effect of OSHA standard on the failure rate

of multi-piece rims has been investigated. The main contributions of this work are:

1. Establishment of the similar rotational dislocation of the rim components from actual

multi-piece rim components and finite element simulations.

2. Documenting/modeling the failure data of different types of rims into statistical

distributions.

3. Looking into the effect of the OSHA standard 1910.177 (Servicing multi-piece rims)

on the failure rates of different multi-piece rims.

5.2 CONCLUSIONS

From the ANSYS simulation results, the dislocation of the side ring was very similar to

that observed in an actual failed multi-piece rim. The inflation pressure and the radial force

developed on the side flange cause it to move out of its desired location. The weakening

and movement of the tire bead also adds to the causes for the dislocation of the side ring.

The maximum deformation obtained from the ANSYS simulation is taken and the side

ring is regenerated in Pro/E. The stresses caused a permanent deformation in the contour of

the side ring. This is incorporated into the regeneration. The figures from Pro/E are shown

below. The dislocation of the side ring is clearly evident from the plots. The effect of

rotating the ring component on the rim base only changes the dislocation from one position

to another. The designer intent fit is no longer present. This assembly when used to mount

a tire and operate on a vehicle could lead to a catastrophic blowout. The huge number of

47

accidents each year provides enough reason to re-look into the design of the multi-piece

rim components. The rotation and separation of components is very dangerous when it is

not contained. This could only be safe if it is restricted to being only on the truck. The

separation and the subsequent blow-off of the rim components results in a much more

extensive damage than the one that is contained to being on the truck itself.

Figure 5.1: Regenerated side ring and rim base assembly.

Figure 5.2: Dislocation of side ring on regenerated assembly.

48

The failure data from different types of rims have been modeled into statistical

distributions and the best fit distribution has been established using the Anderson-Darling

test and the Correlation Coefficient method. The 3 parameter Weibull has been identified

as the best fit distribution to model the data. The shape parameters for all the types of rims

are greater than 1, which evidently proves an increasing failure rate. The survival function

for different type of rims show that the rims have a decreasing survival trend and the

hazard functions show that the hazard rate is increasing.

The failure rate for the RH 5 degree rims has increased from 0.546289 during the pre-

OSHA standard period (1972-1979) to 0.863966 during the post-OSHA standard period

(1980-1987). The corresponding values for the two-piece rim data increased from 0.01606

to 0.745866. The failure rate of the three-piece rims from the available data during the time

when the OSHA standard was not in effect was 0.266757. The value for the failure rate

after the standard came into effect for the three-piece rims is 1.261069. Similarly the

failure rate values for the unknown rims increased from 0.484256 to 0.999762. The

increase in the failure rate has been particularly drastic for the two-piece rims. The finite

element analysis of the two-piece rim suggests the possible reason for this. The dislocation

due to the ambient conditions causes the failure in most cases.

The probable reasons for the increasing failure rates could be because of the material

properties of the components, i.e. the properties of steel, manufacturing and design defects,

operator inefficiency and wear-out period failures. The material properties influence the

change in the shape and contour of the components. The steel components when exposed

to a consistent pressure loading after a considerable period of time could fail. The wear-out

period of a rim also could be a possible reason for the increasing failure rates. The

manufacturing and design defects also account for the increasing failure rates. Since the

design of the multi-piece rims is based on a concentric fit, small tolerance defects could

49

sufficiently transform into major problems while operation. Also the lack of proper

training to the personnel operating on the multi-piece rims leads to failure. Even though

there are regulations for a standardized working environment, improper training could

often lead to a catastrophic failure. Products with similar increasing failure rates have been

looked into, to focus on the reasons for such a trend or behavior. Electronic products like

laser diodes, load-sharing power supplies and military equipment were some of the

products which were found to have increasing failure rates. The reasons for such a trend

varied from manufacturing and design defects, operator inefficiency to wear-out period

failures. In some cases material properties also influenced failure rates for these products.

The non-constant failure rate from the multi-piece rim data suggests that more inspection

is needed along with new warnings. A small defect identified at an earlier stage can

prevent a major failure.

The OSHA standard on servicing multi-piece rims which essentially has safety precautions

like the usage of a cage during inflation, utilization of the proper tools for mounting and

de-mounting the tire rim assembly, training of the workers on the exact procedure for

handling the multi-piece rims has not had a positive effect. The situation had become

worse indicating that more regulations and need for an effective inspection method be part

of the OSHA standard. More investigation should also be carried out into the design

features of the multi-piece rims and the method used for the rim components’ assembly.

The concentric fit of the components allows great risk in its handling and operation. A

bolted type of multi-piece rim design could be investigated for effective functioning. The

B-52 airplanes used by the military have the bolted type of rims in which the failure of the

assembly contains the separation and do not lead to a blow-off of the components.

50

APPENDIX A

POST PROCESSING FROM MINITAB

RH 5 degree rims accident data

Pre OSHA Standard (1972-1979) Distribution ID Plot: Pre OSHA (Years) Using frequencies in Failures_Pre Goodness-of-Fit Anderson-Darling Correlation Distribution (adj) Coefficient Weibull 3.990 0.964 Lognormal 7.450 0.925 Exponential 40.151 * Loglogistic 8.256 0.915 3-Parameter Weibull 3.904 0.965 3-Parameter Lognormal 4.380 0.959 2-Parameter Exponential 26.701 * 3-Parameter Loglogistic 6.189 0.941 Smallest Extreme Value 5.930 0.947 Normal 4.340 0.959 Logistic 6.148 0.941 Table of Percentiles Standard 95% Normal CI Distribution Percent Percentile Error Lower Upper Weibull 1 0.670191 0.127203 0.461997 0.972206 Lognormal 1 1.16914 0.101072 0.986920 1.38501 Exponential 1 0.0356056 0.0025348 0.0309685 0.0409371 Loglogistic 1 1.03850 0.121927 0.825027 1.30720 3-Parameter Weibull 1 0.520149 0.153743 0.218819 0.821479 3-Parameter Lognormal 1 -0.0100495 0.336319 -0.669224 0.649124 2-Parameter Exponential 1 1.02044 0.0022363 1.01607 1.02484 3-Parameter Loglogistic 1 -0.404587 0.380011 -1.14939 0.340220 Smallest Extreme Value 1 -1.88167 0.567364 -2.99368 -0.769656 Normal 1 -0.0963191 0.350049 -0.782403 0.589765 Logistic 1 -0.512780 0.398322 -1.29348 0.267918 Weibull 5 1.42775 0.184931 1.10764 1.84036 Lognormal 5 1.71780 0.120037 1.49793 1.96994 Exponential 5 0.181718 0.0129369 0.158052 0.208928 Loglogistic 5 1.73701 0.152663 1.46215 2.06354 3-Parameter Weibull 5 1.41418 0.203340 1.01564 1.81272 3-Parameter Lognormal 5 1.43766 0.272442 0.903681 1.97163 2-Parameter Exponential 5 1.14538 0.0114135 1.12322 1.16797 3-Parameter Loglogistic 5 1.50627 0.291899 0.934155 2.07838 Smallest Extreme Value 5 0.913260 0.404923 0.119625 1.70689 Normal 5 1.40506 0.280570 0.855151 1.95496 Logistic 5 1.47788 0.300158 0.889585 2.06618 Weibull 10 1.99390 0.206749 1.62720 2.44323 Lognormal 10 2.10889 0.131114 1.86695 2.38219 Exponential 10 0.373264 0.0265734 0.324651 0.429155 Loglogistic 10 2.19245 0.165816 1.89039 2.54276 3-Parameter Weibull 10 2.03854 0.218509 1.61027 2.46681 3-Parameter Lognormal 10 2.21732 0.242278 1.74246 2.69217

51

2-Parameter Exponential 10 1.30916 0.0234443 1.26400 1.35592 3-Parameter Loglogistic 10 2.38331 0.256308 1.88096 2.88567 Smallest Extreme Value 10 2.14757 0.335449 1.49010 2.80504 Normal 10 2.20544 0.248006 1.71935 2.69152 Logistic 10 2.37900 0.261349 1.86676 2.89124 Weibull 50 4.77880 0.222086 4.36275 5.23452 Lognormal 50 4.34805 0.208223 3.95851 4.77593 Exponential 50 2.45563 0.174821 2.13582 2.82333 Loglogistic 50 4.34805 0.217149 3.94261 4.79518 3-Parameter Weibull 50 4.85375 0.214188 4.43395 5.27355 3-Parameter Lognormal 50 5.01206 0.187311 4.64494 5.37918 2-Parameter Exponential 50 3.08968 0.154236 2.80170 3.40726 3-Parameter Loglogistic 50 5.00665 0.194452 4.62553 5.38777 Smallest Extreme Value 50 5.37787 0.176115 5.03269 5.72305 Normal 50 5.02878 0.186862 4.66254 5.39502 Logistic 50 5.02878 0.193934 4.64867 5.40888 Table of MTTF Standard 95% Normal CI Distribution Mean Error Lower Upper Weibull 5.01666 0.206433 4.62795 5.43803 Lognormal 5.09936 0.259940 4.61451 5.63515 Exponential 3.54273 0.252214 3.08134 4.07321 Loglogistic 5.12897 0.249905 4.66183 5.64293 3-Parameter Weibull 5.00251 0.197609 4.61520 5.38981 3-Parameter Lognormal 5.03357 0.187351 4.66637 5.40077 2-Parameter Exponential 4.01920 0.222515 3.60590 4.47986 3-Parameter Loglogistic 5.02964 0.194238 4.64894 5.41034 Smallest Extreme Value 5.01657 0.190568 4.64306 5.39008 Normal 5.02878 0.186862 4.66254 5.39502 Logistic 5.02878 0.193934 4.64867 5.40888

Post OSHA Standard (1980-1987)

Distribution ID Plot: Post OSHA (Years) Using frequencies in Failures_Post Goodness-of-Fit Anderson-Darling Correlation Distribution (adj) Coefficient Weibull 5.395 0.956 Lognormal 5.809 0.960 Exponential 40.943 * Loglogistic 7.360 0.946 3-Parameter Weibull 4.390 0.959 3-Parameter Lognormal 4.529 0.960 2-Parameter Exponential 19.665 * 3-Parameter Loglogistic 6.667 0.953 Smallest Extreme Value 19.910 0.904 Normal 5.328 0.965 Logistic 7.218 0.948

52

Table of Percentiles Standard 95% Normal CI Distribution Percent Percentile Error Lower Upper Weibull 1 0.514905 0.0656523 0.401048 0.661087 Lognormal 1 0.845605 0.0651418 0.727101 0.983423 Exponential 1 0.0306260 0.0018391 0.0272254 0.0344514 Loglogistic 1 0.753826 0.0692144 0.629674 0.902457 3-Parameter Weibull 1 0.716343 0.284941 0.441409 1.56209 3-Parameter Lognormal 1 0.229242 0.231826 -0.225129 0.683613 2-Parameter Exponential 1 1.01551 0.0016106 1.01236 1.01868 3-Parameter Loglogistic 1 0.0883854 0.198341 -0.300355 0.477126 Smallest Extreme Value 1 -2.16217 0.335752 -2.82023 -1.50411 Normal 1 -0.820507 0.269383 -1.34849 -0.292527 Logistic 1 -1.20988 0.286200 -1.77082 -0.648941 Weibull 5 1.10542 0.100044 0.925746 1.31997 Lognormal 5 1.27133 0.0785693 1.12630 1.43504 Exponential 5 0.156304 0.0093864 0.138949 0.175827 Loglogistic 5 1.29525 0.0886384 1.13267 1.48116 3-Parameter Weibull 5 1.14773 0.149299 0.889431 1.48103 3-Parameter Lognormal 5 1.04064 0.157726 0.731501 1.34978 2-Parameter Exponential 5 1.12022 0.0082198 1.10422 1.13644 3-Parameter Loglogistic 5 1.10477 0.151718 0.807410 1.40213 Smallest Extreme Value 5 0.341027 0.253044 -0.154931 0.836985 Normal 5 0.598616 0.215880 0.175500 1.02173 Logistic 5 0.670189 0.210761 0.257104 1.08327 Weibull 10 1.54903 0.115711 1.33806 1.79326 Lognormal 10 1.58003 0.0863745 1.41949 1.75872 Exponential 10 0.321061 0.0192803 0.285412 0.361164 Loglogistic 10 1.65488 0.0976803 1.47409 1.85784 3-Parameter Weibull 10 1.51284 0.107819 1.31562 1.73963 3-Parameter Lognormal 10 1.53798 0.136078 1.27127 1.80469 2-Parameter Exponential 10 1.25747 0.0168842 1.22481 1.29101 3-Parameter Loglogistic 10 1.65868 0.137937 1.38832 1.92903 Smallest Extreme Value 10 1.44650 0.217517 1.02018 1.87283 Normal 10 1.35515 0.190800 0.981184 1.72911 Logistic 10 1.52124 0.182358 1.16383 1.87866 Weibull 50 3.74581 0.145377 3.47144 4.04186 Lognormal 50 3.40160 0.140450 3.13717 3.68833 Exponential 50 2.11220 0.126842 1.87767 2.37603 Loglogistic 50 3.40160 0.142418 3.13362 3.69251 3-Parameter Weibull 50 3.62976 0.216814 3.22875 4.08059 3-Parameter Lognormal 50 3.73692 0.154168 3.43476 4.03908 2-Parameter Exponential 50 2.74966 0.111078 2.54035 2.97622 3-Parameter Loglogistic 50 3.71884 0.143504 3.43758 4.00010 Smallest Extreme Value 50 4.33963 0.132087 4.08074 4.59851 Normal 50 4.02381 0.143697 3.74217 4.30545 Logistic 50 4.02381 0.146217 3.73723 4.31039 Table of MTTF Standard 95% Normal CI Distribution Mean Error Lower Upper Weibull 3.93917 0.134910 3.68343 4.21266 Lognormal 4.06842 0.181244 3.72825 4.43962 Exponential 3.04726 0.182994 2.70890 3.42788 Loglogistic 4.08715 0.179151 3.75068 4.45380 3-Parameter Weibull 3.95489 0.148523 3.67424 4.25697 3-Parameter Lognormal 4.01488 0.147623 3.72554 4.30421 2-Parameter Exponential 3.52865 0.160251 3.22814 3.85714 3-Parameter Loglogistic 4.01263 0.151047 3.71659 4.30868 Smallest Extreme Value 4.01604 0.140675 3.74032 4.29176

53

Normal 4.02381 0.143697 3.74217 4.30545 Logistic 4.02381 0.146217 3.73723 4.31039

Two-piece rims accident data

Pre OSHA Standard (1972-1979)

Distribution ID Plot: Pre OSHA (Year) Using frequencies in Failures_Pre Goodness-of-Fit Anderson-Darling Correlation Distribution (adj) Coefficient Weibull 2.070 0.960 Lognormal 3.436 0.892 Exponential 18.499 * Loglogistic 3.583 0.892 3-Parameter Weibull 1.594 0.971 3-Parameter Lognormal 2.214 0.943 2-Parameter Exponential 14.759 * 3-Parameter Loglogistic 2.523 0.933 Smallest Extreme Value 1.592 0.970 Normal 2.190 0.944 Logistic 2.500 0.934 Table of Percentiles Standard 95% Normal CI Distribution Percent Percentile Error Lower Upper Weibull 1 1.13910 0.382902 0.589436 2.20135 Lognormal 1 1.89389 0.226332 1.49841 2.39375 Exponential 1 0.0397497 0.0049407 0.0311554 0.0507148 Loglogistic 1 1.67821 0.314732 1.16202 2.42371 3-Parameter Weibull 1 0.0648047 0.835550 -1.57284 1.70245 3-Parameter Lognormal 1 1.22895 0.551524 0.147984 2.30992 2-Parameter Exponential 1 1.02434 0.0043552 1.01584 1.03291 3-Parameter Loglogistic 1 0.756045 0.713123 -0.641652 2.15374 Smallest Extreme Value 1 -0.788502 1.13662 -3.01624 1.43924 Normal 1 1.18056 0.568649 0.0660279 2.29509 Logistic 1 0.691576 0.736683 -0.752297 2.13545 Weibull 5 2.12048 0.472446 1.37021 3.28159 Lognormal 5 2.56254 0.248144 2.11955 3.09811 Exponential 5 0.202868 0.0252156 0.159006 0.258830 Loglogistic 5 2.53942 0.352256 1.93490 3.33280 3-Parameter Weibull 5 2.02686 0.865287 0.330930 3.72279 3-Parameter Lognormal 5 2.55357 0.445094 1.68120 3.42594 2-Parameter Exponential 5 1.16526 0.0222273 1.12250 1.20965 3-Parameter Loglogistic 5 2.54616 0.538367 1.49098 3.60134 Smallest Extreme Value 5 1.87642 0.781661 0.344391 3.40844 Normal 5 2.53913 0.454779 1.64778 3.43048 Logistic 5 2.53318 0.548190 1.45875 3.60761 Weibull 10 2.79008 0.485376 1.98398 3.92371 Lognormal 10 3.01074 0.259872 2.54215 3.56570 Exponential 10 0.416707 0.0517949 0.326610 0.531657 Loglogistic 10 3.06312 0.361399 2.43072 3.86004 3-Parameter Weibull 10 3.01459 0.909348 1.23230 4.79688

54

3-Parameter Lognormal 10 3.26526 0.394776 2.49151 4.03901 2-Parameter Exponential 10 1.35000 0.0456567 1.26342 1.44252 3-Parameter Loglogistic 10 3.36509 0.464953 2.45380 4.27639 Smallest Extreme Value 10 3.05331 0.629706 1.81911 4.28751 Normal 10 3.26338 0.401302 2.47685 4.04992 Logistic 10 3.36682 0.470440 2.44477 4.28887 Weibull 50 5.72174 0.383649 5.01712 6.52532 Lognormal 50 5.31632 0.355593 4.66313 6.06102 Exponential 50 2.74144 0.340749 2.14871 3.49767 Loglogistic 50 5.31632 0.379372 4.62243 6.11439 3-Parameter Weibull 50 6.01172 0.459415 5.11128 6.91216 3-Parameter Lognormal 50 5.80688 0.301884 5.21520 6.39856 2-Parameter Exponential 50 3.35840 0.300367 2.81840 4.00186 3-Parameter Loglogistic 50 5.80471 0.315125 5.18708 6.42234 Smallest Extreme Value 50 6.13335 0.292156 5.56073 6.70597 Normal 50 5.81818 0.300534 5.22915 6.40722 Logistic 50 5.81818 0.313564 5.20361 6.43276 Table of MTTF Standard 95% Normal CI Distribution Mean Error Lower Upper Weibull 5.84580 0.357499 5.18547 6.59020 Lognormal 5.86620 0.407716 5.11913 6.72229 Exponential 3.95506 0.491597 3.09993 5.04608 Loglogistic 5.90968 0.392406 5.18852 6.73107 3-Parameter Weibull 5.79615 0.342117 5.12562 6.46669 3-Parameter Lognormal 5.82186 0.301922 5.23011 6.41362 2-Parameter Exponential 4.40688 0.433338 3.63438 5.34357 3-Parameter Loglogistic 5.82097 0.314302 5.20495 6.43699 Smallest Extreme Value 5.78886 0.319662 5.16233 6.41538 Normal 5.81818 0.300534 5.22915 6.40722 Logistic 5.81818 0.313564 5.20361 6.43276


Distribution ID Plot: Post OSHA (Year) Using frequencies in Failures_Post Goodness-of-Fit Anderson-Darling Correlation Distribution (adj) Coefficient Weibull 1.673 0.964 Lognormal 3.117 0.949 Exponential 19.216 * Loglogistic 3.205 0.939 3-Parameter Weibull 1.656 0.964 3-Parameter Lognormal 1.642 0.965 2-Parameter Exponential 11.690 * 3-Parameter Loglogistic 2.044 0.962 Smallest Extreme Value 6.321 0.930 Normal 1.710 0.964 Logistic 2.228 0.960

55

Table of Percentiles Standard 95% Normal CI Distribution Percent Percentile Error Lower Upper Weibull 1 0.510159 0.111582 0.332300 0.783214 Lognormal 1 0.886261 0.105382 0.702019 1.11886 Exponential 1 0.0323338 0.0029634 0.0270174 0.0386964 Loglogistic 1 0.775367 0.120524 0.571737 1.05152 3-Parameter Weibull 1 0.374159 0.793413 -0.340631 1.92922 3-Parameter Lognormal 1 -0.113620 0.578089 -1.24665 1.01941 2-Parameter Exponential 1 1.01710 0.0025960 1.01203 1.02220 3-Parameter Loglogistic 1 -0.409440 0.388820 -1.17151 0.352633 Smallest Extreme Value 1 -2.23479 0.565230 -3.34262 -1.12696 Normal 1 -0.698404 0.430402 -1.54198 0.145168 Logistic 1 -1.15205 0.470541 -2.07429 -0.229803 Weibull 5 1.12572 0.171453 0.835194 1.51730 Lognormal 5 1.33797 0.127620 1.10983 1.61301 Exponential 5 0.165020 0.0151243 0.137887 0.197492 Loglogistic 5 1.34809 0.154470 1.07692 1.68754 3-Parameter Weibull 5 1.09703 0.390058 0.332528 1.86153 3-Parameter Lognormal 5 0.990575 0.337488 0.329111 1.65204 2-Parameter Exponential 5 1.12832 0.0132492 1.10265 1.15459 3-Parameter Loglogistic 5 1.02996 0.295073 0.451628 1.60829 Smallest Extreme Value 5 0.388259 0.418965 -0.432899 1.20942 Normal 5 0.752838 0.343229 0.0801219 1.42555 Logistic 5 0.790498 0.343119 0.117998 1.46300 Weibull 10 1.59671 0.197891 1.25237 2.03574 Lognormal 10 1.66651 0.140599 1.41252 1.96617 Exponential 10 0.338964 0.0310665 0.283231 0.405665 Loglogistic 10 1.73163 0.169202 1.42982 2.09714 3-Parameter Weibull 10 1.61677 0.245676 1.13525 2.09828 3-Parameter Lognormal 10 1.62191 0.263849 1.10478 2.13905 2-Parameter Exponential 10 1.27412 0.0272149 1.22188 1.32859 3-Parameter Loglogistic 10 1.74494 0.260101 1.23516 2.25473 Smallest Extreme Value 10 1.54666 0.356343 0.848242 2.24508 Normal 10 1.52649 0.302180 0.934228 2.11875 Logistic 10 1.66983 0.294046 1.09351 2.24615 Weibull 50 3.98560 0.241887 3.53862 4.48904 Lognormal 50 3.61577 0.230359 3.19132 4.09666 Exponential 50 2.22998 0.204381 1.86332 2.66879 Loglogistic 50 3.61577 0.231932 3.18860 4.10016 3-Parameter Weibull 50 4.04901 0.348364 3.36623 4.73180 3-Parameter Lognormal 50 4.11232 0.261915 3.59898 4.62567 2-Parameter Exponential 50 2.85915 0.179041 2.52891 3.23251 3-Parameter Loglogistic 50 4.10547 0.224142 3.66616 4.54478 Smallest Extreme Value 50 4.57830 0.208509 4.16964 4.98697 Normal 50 4.25556 0.224469 3.81560 4.69551 Logistic 50 4.25556 0.226009 3.81259 4.69853 Table of MTTF Standard 95% Normal CI Distribution Mean Error Lower Upper Weibull 4.21835 0.225733 3.79833 4.68481 Lognormal 4.34035 0.298800 3.79250 4.96733 Exponential 3.21718 0.294859 2.68820 3.85026 Loglogistic 4.38127 0.289059 3.84982 4.98607 3-Parameter Weibull 4.21070 0.224888 3.76993 4.65148 3-Parameter Lognormal 4.25526 0.226042 3.81223 4.69830 2-Parameter Exponential 3.68661 0.258302 3.21357 4.22928 3-Parameter Loglogistic 4.25634 0.227739 3.80998 4.70270 Smallest Extreme Value 4.23923 0.222901 3.80235 4.67610

56

Normal 4.25556 0.224469 3.81560 4.69551 Logistic 4.25556 0.226009 3.81259 4.69853

Three-piece rims accident data


Distribution ID Plot: Pre OSHA (Year) Using frequencies in Failures_Pre

Goodness-of-Fit Anderson-Darling Correlation Distribution (adj) Coefficient Weibull 1.483 0.946 Lognormal 1.871 0.925 Exponential 9.597 * Loglogistic 2.031 0.914 3-Parameter Weibull 1.477 0.947 3-Parameter Lognormal 1.561 0.942 2-Parameter Exponential 4.414 * 3-Parameter Loglogistic 1.758 0.929 Smallest Extreme Value 1.551 0.945 Normal 1.556 0.942 Logistic 1.753 0.929 Table of Percentiles Standard 95% Normal CI Distribution Percent Percentile Error Lower Upper Weibull 1 1.68110 0.513001 0.924363 3.05735 Lognormal 1 2.42037 0.354606 1.81624 3.22545 Exponential 1 0.0418506 0.0074901 0.0294686 0.0594352 Loglogistic 1 2.19566 0.417062 1.51314 3.18602 3-Parameter Weibull 1 1.17165 0.736520 -0.271903 2.61520 3-Parameter Lognormal 1 1.56845 0.766190 0.0667496 3.07016 2-Parameter Exponential 1 2.99477 0.0048366 2.98531 3.00427 3-Parameter Loglogistic 1 1.07747 0.912922 -0.711821 2.86677 Smallest Extreme Value 1 -0.266147 1.42508 -3.05926 2.52697 Normal 1 1.52749 0.785540 -0.0121356 3.06712 Logistic 1 1.02392 0.937272 -0.813101 2.86094 Weibull 5 2.72156 0.567960 1.80793 4.09689 Lognormal 5 3.08982 0.360986 2.45747 3.88490 Exponential 5 0.213590 0.0382270 0.150397 0.303336 Loglogistic 5 3.06770 0.434679 2.32381 4.04971 3-Parameter Weibull 5 2.58433 0.691516 1.22898 3.93967 3-Parameter Lognormal 5 2.82584 0.613755 1.62291 4.02878 2-Parameter Exponential 5 3.09643 0.0246842 3.04842 3.14519 3-Parameter Loglogistic 5 2.79313 0.687380 1.44589 4.14037 Smallest Extreme Value 5 2.21701 0.991990 0.272749 4.16128 Normal 5 2.81107 0.623800 1.58844 4.03369 Logistic 5 2.77879 0.698176 1.41039 4.14719 Weibull 10 3.36679 0.563277 2.42553 4.67332 Lognormal 10 3.51941 0.361988 2.87687 4.30547 Exponential 10 0.438732 0.0785213 0.308927 0.623077 Loglogistic 10 3.56913 0.434655 2.81126 4.53130

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3-Parameter Weibull 10 3.36243 0.639084 2.10985 4.61501 3-Parameter Lognormal 10 3.50010 0.541021 2.43972 4.56048 2-Parameter Exponential 10 3.22969 0.0507032 3.13183 3.33062 3-Parameter Loglogistic 10 3.57580 0.595175 2.40928 4.74232 Smallest Extreme Value 10 3.31364 0.806594 1.73274 4.89453 Normal 10 3.49533 0.547338 2.42257 4.56810 Logistic 10 3.57317 0.601650 2.39396 4.75238 Weibull 50 5.87533 0.440696 5.07207 6.80579 Lognormal 50 5.57060 0.425565 4.79595 6.47038 Exponential 50 2.88633 0.516577 2.03238 4.09910 Loglogistic 50 5.57060 0.453028 4.74983 6.53320 3-Parameter Weibull 50 5.98495 0.421489 5.15885 6.81105 3-Parameter Lognormal 50 5.90065 0.402354 5.11205 6.68925 2-Parameter Exponential 50 4.67848 0.333567 4.06832 5.38014 3-Parameter Loglogistic 50 5.89934 0.424059 5.06820 6.73048 Smallest Extreme Value 50 6.18361 0.389331 5.42053 6.94668 Normal 50 5.90909 0.401556 5.12206 6.69613 Logistic 50 5.90909 0.423249 5.07954 6.73864 Table of MTTF Standard 95% Normal CI Distribution Mean Error Lower Upper Weibull 5.88070 0.409023 5.13128 6.73959 Lognormal 5.93995 0.467974 5.09005 6.93177 Exponential 4.16410 0.745263 2.93210 5.91376 Loglogistic 5.96534 0.471706 5.10889 6.96536 3-Parameter Weibull 5.87506 0.405114 5.08105 6.66907 3-Parameter Lognormal 5.91125 0.402295 5.12276 6.69973 2-Parameter Exponential 5.43481 0.481236 4.56892 6.46481 3-Parameter Loglogistic 5.91068 0.423589 5.08046 6.74090 Smallest Extreme Value 5.86261 0.424896 5.02983 6.69539 Normal 5.90909 0.401556 5.12206 6.69613 Logistic 5.90909 0.423249 5.07954 6.73864


Distribution ID Plot: Post OSHA (Year) Using frequencies in Failures_Post Goodness-of-Fit Anderson-Darling Correlation Distribution (adj) Coefficient Weibull 1.032 0.975 Lognormal 1.195 0.951 Exponential 6.661 * Loglogistic 1.172 0.957 3-Parameter Weibull 1.083 0.978 3-Parameter Lognormal 0.994 0.979 2-Parameter Exponential 4.292 * 3-Parameter Loglogistic 0.971 0.983 Smallest Extreme Value 2.119 0.940 Normal 1.049 0.973 Logistic 0.992 0.977 Table of Percentiles

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Standard 95% Normal CI Distribution Percent Percentile Error Lower Upper Weibull 1 0.755502 0.274315 0.370829 1.53921 Lognormal 1 1.22743 0.256207 0.815304 1.84787 Exponential 1 0.0310432 0.0060998 0.0211208 0.0456270 Loglogistic 1 1.05364 0.314455 0.587019 1.89116 3-Parameter Weibull 1 0.550943 2.62315 -0.702802 5.69222 3-Parameter Lognormal 1 0.664213 0.530357 -0.375267 1.70369 2-Parameter Exponential 1 1.01530 0.0051733 1.00521 1.02549 3-Parameter Loglogistic 1 0.316043 0.630685 -0.920076 1.55216 Smallest Extreme Value 1 -1.27672 0.842964 -2.92890 0.375454 Normal 1 0.121780 0.762681 -1.37305 1.61661 Logistic 1 -0.410128 0.944640 -2.26159 1.44133 Weibull 5 1.42332 0.358726 0.868497 2.33257 Lognormal 5 1.68948 0.279035 1.22228 2.33528 Exponential 5 0.158433 0.0311311 0.107793 0.232864 Loglogistic 5 1.64688 0.349334 1.08669 2.49584 3-Parameter Weibull 5 1.37822 1.33695 -0.702802 3.99859 3-Parameter Lognormal 5 1.49098 0.463182 0.583159 2.39880 2-Parameter Exponential 5 1.11912 0.0264025 1.06855 1.17208 3-Parameter Loglogistic 5 1.43088 0.515943 0.419652 2.44211 Smallest Extreme Value 5 0.843952 0.640907 -0.412203 2.10011 Normal 5 1.25789 0.600239 0.0814417 2.43434 Logistic 5 1.17410 0.659290 -0.118086 2.46628 Weibull 10 1.88268 0.385549 1.26027 2.81250 Lognormal 10 2.00321 0.289443 1.50916 2.65898 Exponential 10 0.325435 0.0639458 0.221416 0.478321 Loglogistic 10 2.01589 0.354452 1.42824 2.84533 3-Parameter Weibull 10 1.90014 0.805693 0.321009 3.47927 3-Parameter Lognormal 10 1.96872 0.426243 1.13330 2.80414 2-Parameter Exponential 10 1.25522 0.0542329 1.15330 1.36614 3-Parameter Loglogistic 10 1.99296 0.457363 1.09655 2.88938 Smallest Extreme Value 10 1.78049 0.554703 0.693298 2.86769 Normal 10 1.86354 0.522794 0.838886 2.88820 Logistic 10 1.89123 0.543962 0.825086 2.95738 Weibull 50 3.91463 0.398114 3.20719 4.77812 Lognormal 50 3.65310 0.382966 2.97459 4.48638 Exponential 50 2.14098 0.420688 1.45665 3.14679 Loglogistic 50 3.65310 0.378327 2.98201 4.47523 3-Parameter Weibull 50 3.97253 0.533363 2.92716 5.01790 3-Parameter Lognormal 50 3.88584 0.368806 3.16300 4.60869 2-Parameter Exponential 50 2.73481 0.356788 2.11776 3.53164 3-Parameter Loglogistic 50 3.88413 0.362828 3.17300 4.59526 Smallest Extreme Value 50 4.23151 0.350784 3.54399 4.91904 Normal 50 4 0.372772 3.26938 4.73062 Logistic 50 4 0.367224 3.28025 4.71975 Table of MTTF Standard 95% Normal CI Distribution Mean Error Lower Upper Weibull 4.00801 0.373070 3.33963 4.81016 Lognormal 4.07747 0.452456 3.28048 5.06809 Exponential 3.08877 0.606924 2.10151 4.53985 Loglogistic 4.13318 0.447815 3.34241 5.11103 3-Parameter Weibull 3.99124 0.360436 3.28479 4.69768 3-Parameter Lognormal 4.01437 0.375941 3.27754 4.75120 2-Parameter Exponential 3.50723 0.514737 2.63050 4.67617 3-Parameter Loglogistic 4.02677 0.372038 3.29759 4.75596 Smallest Extreme Value 3.95737 0.370926 3.23037 4.68438

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Normal 4.00000 0.372772 3.26938 4.73062 Logistic 4.00000 0.367224 3.28025 4.71975

Unknown rims accident data


Distribution ID Plot: Pre OSHA (Years) Using frequencies in Failures_Pre Goodness-of-Fit Anderson-Darling Correlation Distribution (adj) Coefficient Weibull 7.806 0.944 Lognormal 11.645 0.911 Exponential 40.024 * Loglogistic 13.698 0.896 3-Parameter Weibull 7.804 0.945 3-Parameter Lognormal 8.503 0.935 2-Parameter Exponential 27.601 * 3-Parameter Loglogistic 11.350 0.914 Smallest Extreme Value 9.344 0.926 Normal 8.418 0.936 Logistic 11.264 0.914 Table of Percentiles Standard 95% Normal CI Distribution Percent Percentile Error Lower Upper Weibull 1 0.566422 0.110008 0.387101 0.828812 Lognormal 1 1.02449 0.0906152 0.861433 1.21842 Exponential 1 0.0364006 0.0024884 0.0318361 0.0416197 Loglogistic 1 0.909027 0.107313 0.721257 1.14568 3-Parameter Weibull 1 0.686747 0.0901321 0.530984 0.888204 3-Parameter Lognormal 1 -0.299864 0.337472 -0.961298 0.361569 2-Parameter Exponential 1 1.02125 0.0022052 1.01694 1.02558 3-Parameter Loglogistic 1 -0.691519 0.386886 -1.44980 0.0667627 Smallest Extreme Value 1 -2.30617 0.602690 -3.48742 -1.12492 Normal 1 -0.384327 0.348794 -1.06795 0.299298 Logistic 1 -0.799592 0.405099 -1.59357 -0.0056135 Weibull 5 1.28256 0.170922 0.987732 1.66538 Lognormal 5 1.55656 0.111708 1.35231 1.79164 Exponential 5 0.185776 0.0127000 0.162480 0.212412 Loglogistic 5 1.58485 0.142530 1.32873 1.89033 3-Parameter Weibull 5 1.29310 0.153927 1.02402 1.63289 3-Parameter Lognormal 5 1.25011 0.274501 0.712095 1.78812 2-Parameter Exponential 5 1.14950 0.0112544 1.12765 1.17177 3-Parameter Loglogistic 5 1.34538 0.302206 0.753063 1.93769 Smallest Extreme Value 5 0.689099 0.428208 -0.150173 1.52837 Normal 5 1.22190 0.281240 0.670680 1.77312 Logistic 5 1.31921 0.310567 0.710515 1.92791 Weibull 10 1.84003 0.197094 1.49159 2.26987 Lognormal 10 1.94538 0.124571 1.71593 2.20552

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Exponential 10 0.381598 0.0260867 0.333746 0.436311 Loglogistic 10 2.03829 0.159651 1.74822 2.37650 3-Parameter Weibull 10 1.79716 0.184764 1.46918 2.19836 3-Parameter Lognormal 10 2.08479 0.244957 1.60469 2.56490 2-Parameter Exponential 10 1.31762 0.0231174 1.27308 1.36372 3-Parameter Loglogistic 10 2.27998 0.267958 1.75479 2.80517 Smallest Extreme Value 10 2.01188 0.353456 1.31912 2.70464 Normal 10 2.07817 0.249751 1.58867 2.56768 Logistic 10 2.27834 0.273097 1.74308 2.81360 Weibull 50 4.73206 0.229492 4.30298 5.20392 Lognormal 50 4.27177 0.212661 3.87465 4.70959 Exponential 50 2.51046 0.171620 2.19565 2.87041 Loglogistic 50 4.27177 0.230007 3.84394 4.74722 3-Parameter Weibull 50 4.65006 0.236799 4.20836 5.13813 3-Parameter Lognormal 50 5.07654 0.191742 4.70073 5.45235 2-Parameter Exponential 50 3.14534 0.152085 2.86094 3.45800 3-Parameter Loglogistic 50 5.07439 0.205386 4.67184 5.47694 Smallest Extreme Value 50 5.47373 0.181449 5.11809 5.82936 Normal 50 5.09868 0.191171 4.72400 5.47337 Logistic 50 5.09868 0.204661 4.69756 5.49981 Table of MTTF Standard 95% Normal CI Distribution Mean Error Lower Upper Weibull 5.03998 0.212458 4.64031 5.47408 Lognormal 5.15714 0.275334 4.64477 5.72603 Exponential 3.62183 0.247595 3.16766 4.14112 Loglogistic 5.18653 0.270093 4.68327 5.74386 3-Parameter Weibull 5.05801 0.223246 4.63885 5.51505 3-Parameter Lognormal 5.09944 0.191768 4.72359 5.47530 2-Parameter Exponential 4.09949 0.219413 3.69124 4.55290 3-Parameter Loglogistic 5.09832 0.205055 4.69642 5.50022 Smallest Extreme Value 5.08653 0.197070 4.70028 5.47278 Normal 5.09868 0.191171 4.72400 5.47337 Logistic 5.09868 0.204661 4.69756 5.49981


Distribution ID Plot: Post OSHA (Years) Using frequencies in Failures_Post

Goodness-of-Fit Anderson-Darling Correlation Distribution (adj) Coefficient Weibull 5.702 0.938 Lognormal 5.589 0.954 Exponential 25.011 * Loglogistic 7.127 0.937 3-Parameter Weibull 5.017 0.940 3-Parameter Lognormal 4.377 0.964 2-Parameter Exponential 17.401 * 3-Parameter Loglogistic 6.193 0.948 Smallest Extreme Value 13.926 0.895

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Normal 4.576 0.961 Logistic 6.170 0.946 Table of Percentiles Standard 95% Normal CI Distribution Percent Percentile Error Lower Upper Weibull 1 0.414904 0.0639976 0.306657 0.561361 Lognormal 1 0.685525 0.0652661 0.568832 0.826157 Exponential 1 0.0280446 0.0020160 0.0243591 0.0322877 Loglogistic 1 0.607725 0.0676976 0.488526 0.756009 3-Parameter Weibull 1 0.632781 0.0414631 0.556517 0.719496 3-Parameter Lognormal 1 -0.121138 0.296160 -0.701600 0.459325 2-Parameter Exponential 1 1.01289 0.0017486 1.00947 1.01633 3-Parameter Loglogistic 1 -0.577042 0.241101 -1.04959 -0.104492 Smallest Extreme Value 1 -2.22653 0.357879 -2.92796 -1.52510 Normal 1 -0.989346 0.299460 -1.57628 -0.402415 Logistic 1 -1.37644 0.318580 -2.00085 -0.752036 Weibull 5 0.918824 0.101145 0.740511 1.14007 Lognormal 5 1.05245 0.0804412 0.906031 1.22253 Exponential 5 0.143129 0.0102888 0.124320 0.164785 Loglogistic 5 1.07350 0.0897909 0.911182 1.26473 3-Parameter Weibull 5 0.981114 0.0792592 0.837443 1.14943 3-Parameter Lognormal 5 0.722732 0.196603 0.337397 1.10807 2-Parameter Exponential 5 1.10685 0.0089243 1.08949 1.12448 3-Parameter Loglogistic 5 0.680852 0.191813 0.304905 1.05680 Smallest Extreme Value 5 0.120638 0.271669 -0.411824 0.653100 Normal 5 0.348100 0.239972 -0.122237 0.818437 Logistic 5 0.402656 0.235464 -0.0588443 0.864156 Weibull 10 1.30532 0.119043 1.09167 1.56080 Lognormal 10 1.32268 0.0894741 1.15844 1.51020 Exponential 10 0.293999 0.0211341 0.255363 0.338482 Loglogistic 10 1.38885 0.100784 1.20472 1.60112 3-Parameter Weibull 10 1.28643 0.101118 1.10276 1.50070 3-Parameter Lognormal 10 1.22634 0.164154 0.904600 1.54807 2-Parameter Exponential 10 1.23001 0.0183311 1.19460 1.26647 3-Parameter Loglogistic 10 1.31142 0.173387 0.971585 1.65125 Smallest Extreme Value 10 1.15721 0.234638 0.697325 1.61709 Normal 10 1.06109 0.212086 0.645407 1.47677 Logistic 10 1.20800 0.204212 0.807753 1.60825 Weibull 50 3.27182 0.156883 2.97834 3.59421 Lognormal 50 2.96185 0.151621 2.67910 3.27444 Exponential 50 1.93417 0.139037 1.67999 2.22681 Loglogistic 50 2.96185 0.156095 2.67118 3.28415 3-Parameter Weibull 50 3.14244 0.162176 2.84013 3.47694 3-Parameter Lognormal 50 3.35668 0.170388 3.02272 3.69063 2-Parameter Exponential 50 2.56898 0.120597 2.34316 2.81656 3-Parameter Loglogistic 50 3.41752 0.160852 3.10226 3.73279 Smallest Extreme Value 50 3.87000 0.145332 3.58515 4.15485 Normal 50 3.57616 0.159708 3.26314 3.88918 Logistic 50 3.57616 0.164166 3.25440 3.89792 Table of MTTF Standard 95% Normal CI Distribution Mean Error Lower Upper Weibull 3.46587 0.145488 3.19213 3.76308 Lognormal 3.60985 0.200718 3.23712 4.02548 Exponential 2.79041 0.200588 2.42371 3.21260 Loglogistic 3.63098 0.201545 3.25669 4.04829 3-Parameter Weibull 3.46723 0.154205 3.17779 3.78303

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3-Parameter Lognormal 3.56602 0.160503 3.25144 3.88060 2-Parameter Exponential 3.26799 0.173985 2.94417 3.62742 3-Parameter Loglogistic 3.56691 0.164545 3.24441 3.88941 Smallest Extreme Value 3.56658 0.154367 3.26403 3.86914 Normal 3.57616 0.159708 3.26314 3.88918 Logistic 3.57616 0.164166 3.25440 3.89792

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APPENDIX B

Figure B.1: Tire rim assembly

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Figure B.2: Dislocation along a portion of the rim circumference.

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REFERENCES

1. Bradley, J.N., “The Development of the Modern Truck Disc Wheel,” Society of

Automotive Engineers, 700057, 1970.

2. Ridha, R.A., “Finite Element Stress Analysis of Automotive Wheels,” Society

of Automotive Engineers, 760085, 1976.

3. Morita, Y., Kawashima, H., Ishihara, K., and Komatsu, H., “Finite Element

Analysis of Automotive Steel Road Wheel,” Sumitomo Search, No.35, pp.89-106,

1987.

4. Stearns, J., “Stress and Displacement Distribution in Aluminum Alloy

Automobile Rim,” Ph.D Dissertation, University of Akron, 2001.

5. Ridder, R.L., Landgraf, R.W., and Thangjitham, S., “Reliability Analysis of an

Automotive Wheel Assembly,” Society of Automotive Engineers, 930406, 1993.

6. Charles B. Watkins, Steven W. Blate, “Advances in Truck Rim Technology,”

SAE Technical Paper Series, 820810, 1982.

7. Cook, R.D., Malkus, D.S., and Plesha, M.E., “Concepts and Applications of

Finite Element Analysis” J Wiley and Sons, pp. 14-15, 2000.

8. ANSYS, Inc., “Element Library,” Theory Reference.

9. Stephens, M. A., “EDF Statistics for Goodness of Fit and Some Comparisons,”

Journal of the American Statistical Association, Vol. 69, pp. 730-737, 1974.

10. Exhibit for Civil Action No. 88-C-1374, In the Circuit Court of Kanawha

County, West Virginia, 1990.

11. 1910.177, “Servicing multi-piece and single piece rim wheels,” Materials

Handling and Storage, Occupational Safety and Health Standards (OSHA).

12. MINITAB, Inc., “Meet MINITAB,” Documentation for MINITAB Release 14.

66

VITA

Date and Place of Birth

• February 7, 1981 at Guntur, Andhra Pradesh, INDIA.

Education

• Bachelor of Technology (B.Tech) in Mechanical Engineering, JNTU College of

Engineering, Jawaharlal Nehru Technological University, Hyderabad, INDIA.

Work Experience

• Teaching Assistant, Department of Mechanical Engineering, University of

Kentucky, Lexington, KY. (August 2002- May 2004).

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